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Question 2 I Pause Q Zoom Q Review / A A A \( A B C \) Avery was selling concessions at the basketball game. She is selling pizza by the slice for \( \$ 3.50 \) and sports drinks for \( \$ 2.00 \). She sold a total of 96 slices of pizza and sports drinks combined. Av made a total of \( \$ 300 \). Select ALL that apply A. Avery sold 26 slices of pizza and 70 sports drinks. B. Avery sold 72 slices of pizza and 24 sports drinks. C. \( p+s=96 \) D. \( p+s=300 \) E. \( 3 \cdot 50 p+2 s=300 \)

Ask by Santiago Brewer. in the United States
Jan 24,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

Avery sold 72 slices of pizza and 24 sports drinks, \( p + s = 96 \), and \( 3.50p + 2s = 300 \).

Solution

To determine which options apply, let's analyze each one based on the given information: **Given:** - Price per slice of pizza (\( p \)): \$3.50 - Price per sports drink (\( s \)): \$2.00 - Total items sold: \( p + s = 96 \) - Total revenue: \( 3.50p + 2s = 300 \) --- **Option A: Avery sold 26 slices of pizza and 70 sports drinks.** - **Check Total Items:** \( 26 + 70 = 96 \) ✅ - **Check Revenue:** \( 3.50 \times 26 + 2 \times 70 = 91 + 140 = 231 \neq 300 \) ❌ **Result:** **Incorrect** --- **Option B: Avery sold 72 slices of pizza and 24 sports drinks.** - **Check Total Items:** \( 72 + 24 = 96 \) ✅ - **Check Revenue:** \( 3.50 \times 72 + 2 \times 24 = 252 + 48 = 300 \) ✅ **Result:** **Correct** --- **Option C: \( p + s = 96 \)** - **Given directly in the problem.** **Result:** **Correct** --- **Option D: \( p + s = 300 \)** - **This equation incorrectly represents the total items sold as 300, which should represent revenue instead.** **Result:** **Incorrect** --- **Option E: \( 3.50p + 2s = 300 \)** - **Represents the total revenue correctly.** **Result:** **Correct** --- **Summary of Correct Options:** - **B. Avery sold 72 slices of pizza and 24 sports drinks.** - **C. \( p + s = 96 \)** - **E. \( 3.50p + 2s = 300 \)** **Final Answer:** All options **B**, **C**, and **E** are correct.

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The Deep Dive

Avery's concession stand story reflects the real-life use of systems of linear equations! By setting up two equations based on the problem, you can visually and mathematically unravel how much pizza and how many sports drinks were sold, just like balancing a delicious equation. Imagine the satisfaction of solving for the unknowns after crunching those numbers! To get it right, remember to break down your equations carefully. Common mistakes include confusing the total amount with the total number of items, or miscalculating the relationships between pizza slices and sports drinks. Always double-check your work to avoid those sneaky errors, and don’t hesitate to sketch a quick chart or table to visualize it better!

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